# boat moving in a river

#### hoot

I am looking for an explanation on how to calculate this situation. You are floating in a boat in calm water some distance D miles from a dam. A gate is opened at time T. You know the width and depth of the river, the size of the gate and how far above the low side of the dam it is located. The river has an infinite supply of water. How long does it take the boat to start moving towards the dam? One reply is below. I have looked for a discussion of how the pressure wave and speed of sound affect the boat but haven't found anything yet. Any references out there?

"The current starts to pick up as soon as the pressure change from the gate being opened reaches the boat. The speed of sound in water is about 0.92 miles/second, so the current will start to move at T= D/.92. It will of course be a barely perceptible movement at first."

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#### oz93666

I don't see what the speed of sound has got to do with it ?

Pressure waves do move in water at the speed of sound (in water) , but the waves you are dealing with are surface waves , operating at the boundary between two fluids , (air and water) ... these move much slower ...

Your problem is very complex , I don't think you have enough information to solve it .

1 person

#### Woody

The boat will begin to move when it experiences a slope in the water level.

How quickly will the water surface at the location of the boat change in response to the gate opening?
Certainly this can be no quicker than the speed of sound.

However I believe that Oz is correct,
the change in water level will travel at the speed of a surface wave,
which is slower than the speed of sound.

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#### hoot

thanks for looking

Thanks fellows for the input. I have tried to find a way to determine the time and have not found any discussion anywhere to verify the sound and pressure wave answer. And in this situation, the water level does not change as there is an infinite supply of water. I can calculate the volume of water to the boat and the velocity of the flow out of the gate but i don't think this gets me to a solution. This is what happens when 2 engineers go fishing and the fish are not biting. Who I need to talk to is a dam gate operator.

#### Woody

In many of these sort of problems, it is common to use the incompressibility approximation.
If the water is assumed incompressible, then the motive force can only be the change in gravitational potential due to a level change.

However, if you insist that there is no change in the level,
then the motive force will have to be due to a pressure difference.